Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19149589 | C2 | semidirect |
| 3. C2×C8×Dic173 | C2 | semidirect |
| 5. #26011245 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 10. C2×#14583810 | C4 | semidirect |
| 22. C22⋊C8×C173 | C4 | semidirect |
| 57. C2×Dic173 | M16 | semidirect |
| 59. #13063436 | C22⋊C4 | semidirect |
| 104. C173 | #1753 | semidirect |
| 124. C22⋊C8 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| C2×#19149589 | 2 |
| C2×C8×Dic173 | 2 |
| C4×C22⋊Dic173 | 2 |
| #26011245 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #1753 | 173 |